Compositor Backdrop disappeared
Ok, so this is the solution. I had to switch off Sequencer in the Post Processing tab. I had added an image-sequence to the sequencer at some point, which made the Sequencer rendering take over over normal 3D scene rendering. That is why the RenderLayers' node preview disappeared and consequently the backdrop, as there was nothing to display (from the last node in the hierarchy, I checked other nodes and they did display bits and pieces as should be). I somehow connected this behaviour with the Viewer Border checkbox which I checked and I got confused, but it seems it had nothing to do with it. Now that I have the RenderLayers preview and the backdrop back again, I can't replicate the behaviour of Viewer Borders affecting my backdrop.